Doğrusal Olmayan Sınır Değerli Pantograf Tip Gecikmeli Diferansiyel Denklemlerin Nümerik Çözümleri

Öz

Bu çalışmada doğrusal olmayan sınır değerli pantograf tip gecikmeli diferansiyel denklemlerin çözümünde Daftardar-Jafari Metodunu (DJM), Adomian Ayrıştırma Metodu (ADM) ve Diferansiyel Transformasyon Metoduyla (DTM) karşılaştırdık. Bu 3 metot ta seri formunda çözümler oluştumaktadır. Bu 3 metodun ilk n-terimli yaklaşık çözümlerini 2 nümerik örnekle analiz ederek DJM nin sınır değerli gecikmeli diferansiyel denklemlerin çözümünde ADM ve DTM kadar iyi olup olmadığını araştırdık ve sonuç olarak DJM nin bu tip problemlerde güvenilir bir metot olduğunu gördük.

Anahtar Kelimeler

• gecikmeli diferansiyel denklemler,daftardar-jafari,adomian ayriştırma,diferansiyel transformasyon

Numerical Solutions Of Nonlinear Boundary Value Pantograph Type Delay Differential Equations

Öz

In this paper we compared the Daftardar-Jafari Method (DJM) with Adomian Decomposition Method (ADM) and Differential Transformation Method (DTM) in solving nonlinear boundary value delay differential equations of pantograph type. All these 3 methods provide series solutions to the problems. We analysed the first n-term approximate solutions of these 3 methods with 2 numerical examples to see if DJM is as good as ADM and DTM in solving nonlinear boundary value delay differential equations and we found DJM a reliable method in solving this kind of problems.

Anahtar Kelimeler

• delay differential equations,daftardar-jafari,adomian decomposition,differential transformation

Kaynakça

1. Wazwaz, A.M., Raja, M.A.Z, Syam, M.I. (2016) Reliable Treatment for Solving Boundary Value Problems of Pantograph Delay Differential Equations, Romanian Academy Publishing House, ISSN: 1221-1451
2. Ogunfiditimi, F.O. (2015) Numerical Solution of Delay Differential Equations Using the Adomian Decomposition Method (ADM), The International Journal of Engineering And Sciences (IJES), Vol:4, Issue: 5, 18-23.
3. Cakir, M. and Arslan, D. (2015) The Adomian Decomposition Method and The Differential Transform Method For Numerical Solution of Multi-Pantograph Delay Differential Equations, Applied Mathematics, 6, 1332-1343.
4. Daftardar-Gejji, V. and Jafari, H. (2006) An Iterative Method For Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications 316, 753-763.
5. Cherruault, Y., Adomian, G., Abbaoui, K. and Rach, R. (1995) Further Remarks on Convergence of Decomposition Method. International Journal of Bio-Medical Computing, 38, 89-93.
6. Adomian, G. (1986) Nonlinear Stochastic Operator Equations, Academic Press, New York.
7. Adomian, G. (1994) Solving Frontier Problems of Physics: the Decomposition Method, Kluwer Academic Publishers.
8. Cherruault, Y. (1989) Convergence of Adomian`s Method, Kybernetes, Vol: 18, No:2, 31-38.

9. Bhalekar, S., Daftardar-Gejji, V. (2011) Convergence of the New Iterative Method, International Journal of Differential Equations, Vol:2011, 1-10.